Recovering Subjective Probability Distributions

39 Pages Posted: 8 Feb 2019 Last revised: 14 Jan 2020

See all articles by Akira Yamazaki

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: January 26, 2019


This study proposes a direct estimation method for recovering subjective probability distributions from option prices. We find that the subjective cumulative distribution function and subjective statistics are represented as static portfolios composed of plain vanilla options. The portfolio weights of the options are determined by the levels of the reciprocal of the pricing kernel and their differentiations. Using options data, we investigate the historical behavior of subjective probability distributions of returns on the S&P 500 index. We also analyze subjective equity risk premiums and subjective variance risk premiums, which can be regarded as ex-ante risk premiums.

Keywords: subjective probability distribution; reciprocal kernel; risk aversion; static option portfolio; subjective risk premium

JEL Classification: G12, G17

Suggested Citation

Yamazaki, Akira, Recovering Subjective Probability Distributions (January 26, 2019). Available at SSRN: or

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )


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